Credit networks provide a flexible model of distributed trust, which supports transactions between untrusted counterparties through paths of intermediaries. We extend this model by introducing interest rates (prices on lines of credit), both as a means to incentivize credit issuance and to provide a framework for modeling networks of financial relationships. Including interest rates poses a new constraint on transactions, as intermediaries will route payments only if the interest received covers any interest paid. We account for these constraints in an efficient algorithm for finding the maximum transaction flow between two agents in a financial network. There are generally many feasible payment paths serving a given transaction, and we show that the policy for selecting among such paths can have a substantial effect on liquidity, as measured by steady-state probability of transaction success. Finally, we consider the situation where the transaction source can choose among heuristic path selection mechanisms, in order to maximize their payoff. Through empirical game-theoretic analysis, we find that routing is inefficient due to the positive externality of choices promoting network liquidity. However, agent choices do reflect some consideration of overall network liquidity, in addition to their own interest payments.